Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-20T15:25:40.175Z Has data issue: false hasContentIssue false
  • English
  • Français

184. [I. 1.] The third approximation to the nth root of a number

Published online by Cambridge University Press:  03 November 2016

T. J. I'a. Bromwich
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Mathematical Notes
Information
The Mathematical Gazette , Volume 3 , Issue 55 , January 1906 , pp. 275 - 276
Copyright
Copyright © Mathematical Association 1906

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

page 275 note * To reduce this to the form given, write x = N/an, and multiply both sides by a.

page 276 note * If a, b, n are all greater than 1, an−bn>n(a-b). This is obvious on division if n is an integer ; if n is not an integer we have

if x>l. Thus xn−l>n(x−l). Write x=a/b, and the result follows.